1. ECE 111
SHA-2 Algorithms

2. Flavors of SHA SHA-0 SHA-1 SHA-2 SHA-224 SHA-256 SHA-384 SHA-512
Longer hash value = more secure

3. SHA History
1993
The hash function SHA-0 was issued as a federal standard by NIST
1995
SHA-1 published as the successor to SHA-0
2002
SHA-2 variants
SHA-256, SHA-384, and SHA-512 published
2004
SHA-224 published

4. Comparison Between SHA’s
Algorithm
Output size (bits)
Internal state size (bits)
Block size (bits)
Max message size (bits)
Word size (bits)
Rounds
Operations
Collision
SHA-0
160
512
264 − 1 32 80
+,and,or,xor,rotl
Yes
SHA-1
2^63 attack
SHA- 256/224
256/224
256 64
+,and,or,xor,shr, rotr
None yet
SHA- 512/384
512/384
1024
2128 − 1
SHA-1 consists of 80 steps of operation
Each step is also called a “round”. Usually, more rounds imply more security, and hence harder to break.
In this context, “security” refers to the fact that a birthday attack [HAC] on a message digest of size n produces a collision with a workfactor of approximately 2(n/2).

5. SHA-256
Message is processed in 512-bit blocks sequentially, just like SHA-1
Message digest is 256 bits instead of SHA-1’s 160-bits
64 rounds instead of 80 rounds of compression
Algorithm structure same as SHA-1
Step 1: Padding bits
Step 2: Appending length as 64 bit unsigned
Step 3: Buffer initiation
Step 4: Processing of message
Step 5: Output

6. SHA-256 Algorithm
Buffer initiation: Eight 32-bit words instead of five in SHA-1
H0 = 0x6a09e H1 = 0xbb67ae85 H2 = 0x3c6ef H3 = 0xa54ff53a H4 = 0x510e527f H5 = 0x9b05688c H6 = 0x1f83d9ab H7 = 0x5be0cd19

7. SHA-256 Algorithm Kt constants
K [0..63] = 0x428a2f98, 0x , 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5, 0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3, 0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174, 0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da, 0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x , 0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13, 0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85, 0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd , 0xf40e3585, 0x106aa070, 0x19a4c116, 0x1e376c08, 0x c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3, 0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208, 0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2

8. SHA-256 Algorithm Each step t (0 ≤ t ≤ 63): Word expansion for Wt
If t < 16
Wt = tth 32-bit word of Mj
If 16 ≤ t ≤ 63
S0 = (Wt-15 rightrotate 7)  (Wt-15 rightrotate 18)  (Wt-15 rightshift 3)
S1 = (Wt-2 rightrotate 17)  (Wt-2 rightrotate 19)  (Wt-2 rightshift 10)
Wt = Wt-16 + S0 + Wt-7 + S1

9. SHA-256 Algorithm Each step t (0 ≤ t ≤ 63):
S0 = (A rightrotate 2)  (A rightrotate 13)  (A rightrotate 22)
maj = (A ^ B)  (A ^ B)  (B ^ C)
t2 = S0 + maj
S1 = (E rightrotate 6)  (E rightrotate 11)  (E rightrotate 25)
ch = (E ^ F)  (( E) ^ G)
t1 = H + S1 + ch + Kt + Wt
(A, B, C, D, E, F, G, H) = (t1 + t2, A, B, C, D + t1, E, F, G)

10. SHA-256 Algorithm Finally, when all 64 steps have been processed, set
H0 = H0 + A
H1 = H1 + B
H2 = H2 + C
H3 = H3 + D
H4 = H4 + E
H5 = H5 + F
H6 = H6 + G
H7 = H7 + H
When all Mj have been processed, the 256-bit hash of M is available in H0, H1, H2, H3, H4, H5, H6, and H7

11. SHA-512 SHA-512 is identical in structure, but:
all numbers are 64 bits long,
there are 80 rounds instead of 64,
the initial values and additive constants are extended to 64 bits, and
the shift and rotate amounts used are different.

12. More Information Here is the Wikipedia page.